This invention relates to interferometry, and more particularly to multiple phase shifting interferometry.
Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, to measure the surface profile of a measurement surface, one can use an interferometer to combine a measurement wavefront reflected from the measurement surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined measurement and reference wavefronts caused by variations in the profile of the measurement surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface.
With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and measurement wavefronts to produce a series of optical interference patterns that span a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). In PSI, typically, a single phase shifting device is employed to shift the phase between the reference and measurement wavefronts to produce intensity modulation at a particular frequency.
The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase-offset equal to the phase difference between the combined measurement and reference wavefronts for that spatial location. Using numerical techniques known in the art, such as a Fourier decomposition of the intensity variation, the phase-offset for each spatial location is extracted from the sinusoidal dependence of the intensity values to provide a profile of the measurement surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
Unfortunately, PSI measurements can be complicated by spurious reflections from other surfaces of the measurement object because they too contribute to the optical interference. In particular, light from all locations in the interferometer, including scattering from small surface defects such as scratches, pits or dust (or volume defects such as bubbles) can influence the interferogram. These defects act as light scattering centers, producing characteristic ring patterns called Newton rings or xe2x80x9cBulls eyexe2x80x9d patterns that can imprint onto the measured phase map, thereby affecting the extracted surface topography. In such cases, the net optical interference image is a superposition of multiple interference patterns produced by pairs of wavefronts reflected from the multiple surfaces or defects of the measurement object and the reference surface.
In general, the multi-phase shifting interferometric system extends and improves phase-shifting interferometry by minimizing measurement errors resulting from additional, unwanted reflections of non-measurement surfaces and surface defects that contaminate the optical interference pattern. The multi-phase shifting interferometric system minimizes these measurement errors by exploiting the sensitivity of the PSI extracting algorithms to different modulation frequencies. In particular, each PSI extracting algorithms exhibits a specific frequency dependence whereby certain frequency components, determined by the exact algorithm, are weighted more heavily than other frequency components such that the algorithm suppresses certain frequency components relative to others. The multi-phase shifting interferometric system uses the frequency modulating sensitivity of the PSI extracting algorithms to filter and suppress the contribution of unwanted optical interference in the measured phase by interferometrically modulating the optical interference pattern resulting from additional, unwanted reflections of non-measurement surfaces and surface defects at frequencies that are different from the desired optical interference pattern and fall in frequency regions at which the algorithms exhibit low sensitivity.
The multi-phase shifting interferometric system includes at least two independent phase shifting components that each independently shift the phase in the interferometric cavity. Examples of phase shifting components include, but are not limited to, translatable measurement and reference surfaces, tunable light sources, polarizing optics, and phase shifting components in tandem interferometric systems. Together, the multiple-phase shifting components operate cooperatively to produce an interference modulation for the desired cavity interference at one frequency and an interference modulation due to the interference produced from other undesired sources at a different frequency. The multi-phase shifting interferometric system chooses phase shifting rates so that the undesired interference modulation occurs in frequency regions where the phase extraction algorithm exhibits reduced sensitivity and the desired interference modulation occurs in frequency regions of high algorithm sensitivity.
In general, in a first aspect the invention features a method for performing phase-shifting interferometry, which includes differentially modulating an interference signal derived from an interferometer to cause a first interference component of the interference signal to modulate at a first frequency and a second interference component of the interference signal to modulate at a second frequency, wherein the first interference component of the interference signal originates from an interferometric cavity of,interest in the interferometer and the second interference component of the interference signal originates from a defect in the interferometer.
Embodiments of the invention can further include any of the following features. The method can include differentially modulating the interference signal comprises independently shifting a phase in the interferometric cavity using at least two independent phase shifting components. The interferometric cavity can include a measurement object. The independent phase shifting can include using a first of the phase shifting components to modulate a position of a first surface (e.g., a reference surface or a measurement surface of a measurement object) that defines part of the interference cavity. The independent phase shifting can include using a second of the phase shifting components to modulate the position of a second surface that defines another part of the interference cavity. Moreover, the first surface can be a measurement surface and the second surface can be a reference surface. The desired interference intensity can modulate at a frequency related to:
v1xe2x88x92v2
wherein v1 and v2 are the modulation rates of the first surface and the second surface, respectively.
Furthermore, in some embodiments the independent phase shifting can include using a first of the phase shifting components to modulate a wavelength of an input beam to the interferometer. In such cases, the interference signal phase variation due to the modulation of the wavelength can be related to   2  ⁢  n  ⁢            ∂      k              ∂      t        ⁢      (                  x        1            -              x        2              )  
wherein n is a refractive index,   k  =            2      ⁢      π        λ  
wherein xcex is the wavelength the input beam in the interferometer,       ∂    k        ∂    t  
is a wavelength scan rate, and x1 and x2 are positions of surfaces that define the interferometric cavity. The independent phase shifting further can include using a second of the phase shifting components to modulate x2. The interference signal phase variation due to the wavelength modulation and the position modulation can be related to:       2    ⁢    n    ⁢                  ∂        k                    ∂        t              ⁢          (                        x          1                -                  x          2                    )        -      2    ⁢          nkv      2      
wherein v2 is the rate at which x2 is modulated. Moreover, the method can further include repositioning the surface at x1 to a new position at x1xe2x80x2, and selecting at least one of x1xe2x80x2,       ∂    k        ∂    t  
or v2 so that       x    1    xe2x80x2    =            x      1        +                                        kv            2                    ⁡                      (                                          ∂                k                                            ∂                t                                      )                                    -          1                    .      
One of the surfaces can be a reference surface and the other of the surfaces can be a surface of a measurement object (e.g., a transparent measurement object). The distance between the measurement object and the reference surface can be at least equal to a thickness of the measurement object.
In further embodiments, the method can include any of the following features. The independent phase shifting can include using a first of the phase shifting components to variably sample a plane-polarized component of a polarized interference beam, wherein the interference signal is derived from the polarized interference beam, and the polarized interference beam is retarded by a predetermined amount prior to being variably sampled. The intensity of the normalized sampled component can be related to:       I    ⁡          (              θ        ,        ϕ            )        =            1      -              sin        ⁡                  (                                    2              ⁢                              xe2x80x83                            ⁢              θ                        -            ϕ                    )                      2  
wherein xcex8 is an orientation angle of the sampled component and xcfx86 is a phase difference between a first component and a second component of the polarized interference signal, the first component being polarized orthogonal to the second component, and wherein the polarized interference beam is retarded by a quarter wavelength. The independent phase shifting can include using a second of the phase shifting components to modulate a wavelength of an input beam to the interferometer.
The method for performing phase-shifting interferometry can also include applying a phase extraction algorithm to the interference signal to determine a phase of the interference signal. A first sensitivity of the phase extraction algorithm occurring at the first frequency can be greater than a second sensitivity of the phase extraction algorithm occurring at the second frequency. Additionally, the method can include estimating, from a known geometry of the interferometer, a band of frequencies in which the second interference component could occur. Furthermore, the method can include selecting a first modulation rate of a first of the two independent phase shifting components and a second modulation rate of a second of the two independent phase shifting components, so that a first sensitivity of the phase extraction algorithm occurring at the first frequency is greater than a second sensitivity of the phase extraction algorithm occurring at a second frequency, the second frequency being within the estimated band of frequencies.
The phase-shifting interferometry method can include operating the interferometer in tandem with a second interferometer. The independent phase shifting can include using a first of the phase shifting components to modulate the position of a surface in the second interferometer. Furthermore, the independent phase shifting further can include using a second of the phase shifting components to modulate a wavelength of an input beam to the interferometer.
Furthermore, the interferometric cavity may include a reference surface and a surface of a measurement object. More specifically, a distance between the measurement object and the reference surface may be equal to at least a thickness of the measurement object (e.g., a transparent parallel plate).
The interferometer may be a Fizeau interferometer.
In general, in another aspect, the invention features a system for performing phase-shifting interferometry. The system includes: an interferometer for receiving a light beam to generate an interference signal; an interference cavity of interest included in the interferometer; a detector for recording the interference signal; at least two phase-shifting components for differentially modulating the interference signal; and a system controller connected to the at least two phase shifting components and the detector and which during operation causes the at least two phase-shifting components to modulate a first interference component of the interference signal at a first frequency and a second interference component to modulate at a second frequency, wherein the first interference component of in the interference signal originates from the interference cavity of interest and the second interference component if the interference signal originates from a defect in the interferometer.
Embodiments of the system can include any of the following features. The system can include a first surface that defines part of the interference cavity of interest, and wherein during operation a first of the phase shifting components modulates a position of the first surface. The first surface can be a reference surface or a measurement surface of a measurement object. The system can further include a second surface that defines another part of the interference cavity of interest, wherein during operation a second of the phase shifting components modulates the position of the second surface. The first surface can include a measurement surface and the second surface can include a reference surface.
Furthermore, the system can include a light source for providing a light beam to the interferometer, wherein the light beam has a wavelength, and during operation a first of the phase shifting components modulates the wavelength of the light beam from the light source. Additionally, the system can include a first surface defining a part of the interference cavity of interest, wherein during operation a second of the phase shifting components modulates a position of the first surface (e.g., a reference surface). The system can also include a second surface defining another part of the interference cavity of interest, wherein the first surface is a reference surface and the second surface is a measurement surface of a measurement object (e.g., a transparent measurement object). A distance between the measurement object and the reference surface may be at least equal to a thickness of the measurement object.
In some embodiments, the interferometry system can further include a polarizer positioned in the interferometer between the detector and the interference cavity of interest and a retarder (e.g., a quarter wave retarder) positioned in the interferometer between the polarizer and the interference cavity of interest; wherein the light beam is a polarized light beam and during operation a polarized interference beam is retarded by the retarder and a first of the phase shifting components rotates the polarizer to variably sample a plane-polarized component of the polarized interference beam, wherein the interference signal is derived from the polarized interference beam. Furthermore, the system can include a first surface (e.g., a reference surface) that defines part of the interference cavity of interest, and wherein during operation a second of the phase shifting components modulates a position of the first surface.
The interferometry system can include a second interferometer, the second interferometer positioned to operate in tandem with the interferometer. The second interferometer can include a surface, and during operation a first of the phase shifting components can modulate a position of the first surface. Furthermore, the system can include a light source for providing a light beam to the interferometers, wherein the light beam has a wavelength, and during operation a second of the phase shifting components modulates the wavelength of the light beam from the light source. The first and second interferometers can be any kind of interferometer, for example, a Fizeau interferometer and a Mach-Zehnder interferometer, respectively.
The interferometric cavity of interest in the interferometry system can include a reference surface and a surface of a measurement object (e.g., a transparent parallel plate). A distance between the measurement object and the reference surface can be equal to at least a thickness of the measurement object.
In general, the interferometer in the interferometry system can be any kind of interferometer (e.g., a Fizeau interferometer or a Michelson interferometer).
Embodiments of the invention can have one or more of the following advantages. The multi-interferometric system reduces the influence of coherent artifacts on phase measurements thereby improving the measurement accuracy and repeatability. The multi-interferometric system reduces optical constraints associated with measurements of transparent parallel plates. The multi-interferometric system provides a significantly increased working distance between the reference and transparent parallel plate test surfaces relative to wavelength tuning Fizeau interferometric systems, such as described in U.S. Ser. No. 09/349,593 filed on Jul. 7, 1999. In wavelength tuning Fizeau interferometric systems, thin transparent parallel plates must be positioned relative to the reference surface approximately one half the thickness of the plate so as to suppress correctly interference from the opposite surface, whereas the multi-interferometric system facilitates placement of the thin transparent parallel plate at a distance of several plate thicknesses.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.
FIG. 1 is a graph of the relative sensitivity of a 5-frame phase extraction algorithm as a function of modulation frequency.
FIG. 2 is a graph of the relative sensitivity of a 13-frame phase extraction algorithm as a function of modulation frequency.
FIG. 3 is a schematic diagram of a multi-phase shifting apparatus.
FIG. 4 is an expanded schematic view of the interferometer unit and detector unit of the multi-phase shifting apparatus shown in FIG. 3.
FIG. 5 is a schematic diagram of the multi-phase shifting apparatus of FIG. 3 including defects in the interferometer optics.
FIG. 6 is a schematic of another multi-phase shifting apparatus.
FIG. 7 is a schematic of another multi-phase shifting apparatus.
FIG. 8 is a schematic of another multi-phase shifting apparatus.